1
The largest term common to the sequences 1, 11, 21, 31, ... to 100 terms and 31, 36, 41, 46, ... to ...
2
If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m + n) ...
3
In an A.P. of which a is the first term, if the sum of the first p terms is zero, then the sum of th ...
4
If a, 1/b, c and 1/p, q,1/ r form two arithmetic progressions of the same common difference, then a, ...
5
Suppose that F(n + 1) = (2F(n) + 1)/2 for n = 1, 2, 3, ... and F(1) = 2. Then, F(101) equals ...
6
. Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in ...
7
If (p + q)th term of a G.P. is 'a' and its (pq)th term is 'b' where a, b ∈ R, then its pth term is ...
8
If the sides of a triangle are in G.P., and its largest angle is twice the smallest, then the commo ...
9
The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then the common ratio of the G ...
10
If the sides of a right angled triangle are in A.P. then the sines of the acute angles are ...
11
150 workers were engaged to finish a piece of work in a certain number of days. Four workers stopped ...
12
If a1, a2, a3,... are in A.P., then ap, aq,ar , ... are in A.P. if p, q, r are in ...
13
If a1, a2, a3 (a1 > 0) are three successive terms of a G.P. with common ratio r, the value of r for ...
14
If x, y, z are in G.P. and a^x = b^y = c^z, then ...
15
The geometric mean between -9 and -16 is ...
16
The sum of 20 terms of a series of which every even term is 2 times the term before it, and every od ...
17
If three positive real numbers a, b, c are in A.P. such that abc = 4, then the minimum value of b is ...
18
The maximum sum of the series 20+19 (1/3)+18(2/3)+ is ...
19
If the ratio of the sum to n terms of two A.P.'s is (5n + 3); (3n + 4), then the ratio of their 17th ...
20
If S denotes the sum of first 'n' terms of an A.P. and (S3n - Sn-1)/s2n-s2n-1 = 131, then the value ...
21
The number of terms of an A.P. is even; the sum of the odd terms is 24, and of the even terms is 30, ...
22
Consider an A.P. a1, a2, a3, ... such that a3 + a5 + a8 = 11 and a2 + a4 = -2, then the value of a1 ...
23
If Sn denotes the sum of the first n terms of an A.P. whose first term is a and common difference i ...
24
If (1 + x⁴)(1+x)(1+x^2)....(1+x^128) = summation from r=0to n of xto power r, then n is equal to ...
25
The first term of an infinite geometric series is 21. The second term and the sum of the series are ...
26
The number of terms common between the series 1+2+4+8 to 100 terms and 1+4+7+10 to 100 terms is ...
27
After striking the floor, a certain ball rebounds (4/5) of the height from which it has fallen. Then ...
28
Consider the ten numbers a, ar, ar², ..., ar⁹. If their sum is 18 and the sum of their reciprocals i ...
29
Let a = 111... 1 (55 digits), b = 1+10+10^2 + ... 10^4 , c = 1+10^5 +10^10 +10^15+...+10^50 Then ...
30
In a G.P., the first, third, and fifth terms may be considered as the first, fourth, and sixteenth t ...
31
If a, b, and c are in A.P. then a² + c² - 8b^3 is equal to ...
32
If the sum of n terms of an A.P. is c * n(n - 1), where c ≠ 0, then the sum of the squares of these ...
33
16. If a, b, c,... are in A.P., then a, b, c, d,... are in A.P. if p, q, r are in ...
34
Let a₁, a₂, a₃ be terms of an A.P. If( a₁ + a₂ +... + ap )/( a₁ + a₂ + ... + aq) =p^2/ q², then a6 ...
35
. If |a| < 1 and |b| < 1, then the sum of the series 1 + (1 + a)b + (1 + a + a^2)b^2 + (1 + a + a^2 ...
36
The value of log₂4 is ...
37
If S denotes the sum to infinity and Sn denotes the sum of n terms of the series 1, 1/2, 1/4, 1/8, . ...
38
If a² + b², ab + bc, and b² + c² are in G.P., then a, b, c are in ...
39
Let an be the nth term of a G.P. of positive numbers. If 100, 100, and 4th terms of these ten terms ...
